Game Development Reference
In-Depth Information
Of course, A is all-knowing and purely rational as well, and will therefore have
a pretty good handle on all of the above scenarios. As we saw, if B were in charge of
distribution, C and E would be left out in the cold with nothing at all. A knows
this—and knows that those are the two votes he needs. What's more, he knows that
the price of those votes is simply one gold piece. C and E, being rational, will real-
ize that the one gold coin is better than either nothing at all or, in the case of C,
eventually being thrown off. With all of this in mind, A's proposal is as follows.
Pirate
Gold
Vote
A
98
Yes*
B
0
No
C
1
Yes
D
0
No
E
1
Yes
One final note: like B's option above, A could possibly distribute those two
coins another way, for example, giving one to D instead of C. However, just like E
in the example above, D would rather chuck A overboard as pirates seem inclined
to do and collect his one gold coin from B in the next round. Therefore, A will sim-
ply give the one gold coin to C rather than D.
For those of you who are familiar with recursion, this is a perfect example of
how a problem can be solved by starting with the smallest possible scenario (in
this case, two pirates) and working backward… applying the same rules at each
level, but with the knowledge gained from the prior ones. Given that, if you
have enough gold to support the pirate population, you can solve the Pirate
Game for any number of greedy mateys. (You can even do up to 200 pirates
with 100 gold coins.)
For those of you who are
not
familiar with the definition of
recursion
, this is
the way it was presented to me in my AP computer class in high school.
recursion
n:
1. (see
recursion
)
The lesson to be learned here is that, even when agents are purely rational and
have perfect information on hand (or on hook), sometimes the rational thing to do
needs a little digging to find. In this case, A had to take into account what D, C, and
B would propose (in that order) and how each would vote for each of those propos-
als. All of those issues together get rolled up into what A needs to propose. This is
the normative decision theory approach. We have been told, mathematically and
algorithmically, what we
should
do.
